Search
 
 

STATICS - CASE STUDY

    Introduction


Problem Graphic
 

A car jack is constructed with four pinned members and a threaded shaft. The shaft must be designed to withstand the tension that results when hoisting a heavy automobile.

What is known:

  • The members of the jack are pinned together at points A, B, C, and D.
  • The length of each member is 0.2 m.
  • The weight of the automobile exerts a force of 1,960 N on the jack.
  • The threaded shaft is pinned to the jack at points C and D.
  • Under normal conditions, the jack is designed to support weight when the bottom members are at an angle between θ = 30° and θ = 60°.
     
    Questions


Force Diagram

 

At what angle θ is the tension in the shaft greatest under normal conditions (30o ≤ θ ≤ 60o)? At what angle θ is the tension in the shaft least?

   
  Approach

 
  • Determine the virtual work performed by the weight of the automobile and the tension in the shaft.
  • Knowing that the total virtual work must be equal to zero, derive an equation for the tension T as a function of the angle θ.
  • Use graphic analysis to determine the maximum and minimum values of T under normal operating conditions.
     
   
 
Practice Homework and Test problems now available in the 'Eng Statics' mobile app
Includes over 500 problems with complete detailed solutions.
Available now at the Google Play Store and Apple App Store.